A280042 a(1) = 1, a(n+1) is the numerator of n-th partial fraction of the continued fraction [1; 10, 100, 1000, ..., 10^n].

1, 11, 1101, 1101011, 11010111101, 1101011111201011, 1101011111212021111101, 11010111112121312122121201011, 1101011111212132313223231313121111101, 1101011111212132324233342425242423223121201011

Offset

1,2

Links

Seiichi Manyama, Table of n, a(n) for n = 1..45

Formula

a(n) = 10^(n-1)*a(n-1) + a(n-2).

Example

G.f. = x + 11*x^2 + 1101*x^3 + 1101011*x^4 + 11010111101*x^5 + 1101011111201011*x^6 + ...
a(3) = 1101, the numerator of 1 + 1/(10 + 1/100) = 1101/1001.

Crossrefs

Denominators are in A015482.

Cf. A061377, A280219, A280220.

Sequence in context: A109227 A133342 A110574 * A287044 A191111 A127851

Adjacent sequences: A280039 A280040 A280041 * A280043 A280044 A280045

Keyword

nonn,frac

Author

Seiichi Manyama, Dec 31 2016

Status

approved